Are there restrictions as to the number of pets you can own in Los Angeles?

Contact the Department of Animal Care and Control: http://animalcare.lacounty.gov/

((I just copy and pasted this from http://ordlink.com/codes/lacounty/index.htm ... it was tough to find!))

10.20.038 Residential dogs and cats--Limitations.

A. Dogs. Up to three dogs may be kept at any residence without an animal facility license, provided the dogs' owner or custodian licenses each individual dog and complies with the Mandatory Spay and Neuter Program for Dogs, 10.20.350 et seq. For purposes of this section, a service dog licensed under Section 10.20.090, is not counted toward the number of dogs kept or maintained, while such dog is serving a person who is disabled within the meaning of Government Code Section 12926(i) or Government Code Section 12926(k).
B. Cats. Up to five cats may be kept at any residence without an animal facility license, provided the cats' owner or custodian licenses each individual cat, has each cat spayed or neutered and keeps all cats primarily indoors. (Ord. 2009-0043 § 10, 2009.)